Find the equation of the line perpendicular to the graph of 5x+y=4 that contains the point(-2,1).

Step-by-step explanation:

The equation of a straight line can be represented in the slope intercept form as

y = mx + c

Where

m = slope = (change in the value of y in the y axis) / (change in the value of x in the x axis)

The equation of the given line is

5x + y = 4

Rearranging the equation in the slope intercept form, it becomes

y = - 5x + 4

Comparing with the slope intercept form, slope = - 5

If two lines are perpendicular, it means that the slope of one line is the negative reciprocal of the slope of the other line.

Therefore, the slope of the line contains the point(-2,1) is 1/5

To determine the intercept, we would substitute m = 1/5, x = - 2 and y = 1 into y = mx + c. It becomes

1 = 1/5 × - 2 + c

1 = - 2/5 + c

c = 1 + 2/5 = 7/5

The equation becomes

y = x/5 + 7/5